(3x^2-8x+1)-(-x^2+4)+(6x^3-x)

Jasonbradley

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Jun 16, 2024

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Simplifying Polynomial Expressions: (3x^2-8x+1)-(-x^2+4)+(6x^3-x)

This article will guide you through the process of simplifying the polynomial expression: (3x^2-8x+1)-(-x^2+4)+(6x^3-x).

Understanding the Process

To simplify a polynomial expression, we need to combine like terms. Like terms are terms that have the same variable and exponent. For example, 3x^2 and -x^2 are like terms, while 3x^2 and 3x are not.

Step-by-Step Simplification

1. Distribute the Negative Sign: Begin by distributing the negative sign in front of the second set of parentheses:

   (3x^2 - 8x + 1) + x^2 - 4 + (6x^3 - x)

2. Combine Like Terms: Now, identify and combine like terms:

   6x^3 + (3x^2 + x^2) + (-8x - x) + (1 - 4)

3. Simplify: Combine the coefficients of each like term:

   6x^3 + 4x^2 - 9x - 3

Final Result

The simplified form of the expression (3x^2-8x+1)-(-x^2+4)+(6x^3-x) is 6x^3 + 4x^2 - 9x - 3.

Key Takeaways

• Distribute: Pay attention to negative signs and distribute them correctly.
• Combine: Identify like terms and combine their coefficients.
• Order: While not mandatory, it's common practice to arrange terms in descending order of exponents.